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Phrases Previous Year Questions (PYQs)

Phrases Differentibility PYQ

Phrases PYQ
List I List II
A. Dog : Rabies :: Mosquito : I. Bacteria
B. Amnesia : Memory :: Paralysis : II. Liver
C. Meningitis : Brain :: Cirrhosis : III. Movement
D. Influenza : Virus :: Typhoid : IV. Malaria






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Phrases Previous Year PYQPhrases CUET 2023 PYQ

Solution

Dog causes Rabies, Mosquito causes Malaria → A-IV
Amnesia affects Memory, Paralysis affects Movement → B-III
Meningitis affects Brain, Cirrhosis affects Liver → C-II
Influenza is caused by Virus, Typhoid is caused by Bacteria → D-I

Correct matching: A-IV, B-III, C-II, D-I
Phrases PYQ
Let $f(x)=\, \vert{|x|}-1\vert$, then point(s) where $f(x)$ is not differentiable is (are):





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Phrases Previous Year PYQ Phrases CUET 2022 PYQ

Solution

Phrases PYQ
If $f$ and $g$ are differentiable in $(0,1)$ satisfying $f(0)=2=g(1), g(0)=0, f(1)=6$, then for some $c\in(0,1)$





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

Apply Mean Value Theorem to $f-g$: $\dfrac{(f-g)(1)-(f-g)(0)}{1-0}=\dfrac{(6-2)-(2-0)}{1}=2$ So, $f'(c)-g'(c)=2$ $\Rightarrow f'(c)=2g'(c)$
Phrases PYQ
Which of the following functions is differentiable at $x=0$?





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Phrases Previous Year PYQ Phrases CUET 2023 PYQ

Solution

$|x|$ is not differentiable at $0$.

Near $x=0$, $\sin(|x|)\approx |x|$.

For option (4):
$f(x)=\sin(|x|)-|x|$

Near $0$:
$f(x)\approx |x|-|x|=0$

Both left-hand and right-hand derivatives at $0$ are equal, hence $f(x)$ is differentiable at $0$.

All other options involve $|x|$ in a way that makes the derivative discontinuous at $0$.

Phrases

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